After replacing the 5 caps there is still a defect in the BL7000, which is still unknown. I have the same problem with one of my own BL7000's and it works sometimes, sometimes not.
Replacing the complete display board solves the problem, that's for sure, tested, but this won't help you. There is more than the caps, i believe it has something to do with the acid of the defect caps, the acid has destroyed something else and make a shortcut. I have cleaned these display boards and some work again, some not.
Remove the display itself, yes it can be disassembled by the black plastic straps, clean the board with hot water, isopropanol and hot water again. Let it dry for some days and test it again. Its 50:50 to have removed the acid. Probably its under the smd ir transceiver chip next to the pair of caps.